3D rupture effects (seismogenic depth) Huihui Weng Jean-Paul - - PowerPoint PPT Presentation

3D rupture effects (seismogenic depth)

Huihui Weng Jean-Paul Ampuero ICTP, Trieste, Italy, 2-14 Sep.

Sub-Rayleigh Supershear Rupture speed Rupture speed Unstable vE vP vS vR

Modes II (strike slip)

Subshear vS

Modes III (dip slip)

Rupture speeds in 2D

Sub-Rayleigh Supershear Rupture speed Rupture speed Unstable vE vP vS vR

Modes II (strike slip)

Subshear vS

Modes III (dip slip)

Stable speeds in 2D

velocity term g(v) for energy release rate

Finite seismogenic width

Fault and Rock Mechanics (FARM)

Aseismic stable Aseismic stable Aseismic stable Aseismic stable T r e n c h T r e n c h Seismogenic Zone

S u b d u c t i n g p l a c e S u b d u c t i n g p l a c e

Weng and Ampuero, 2019

Elongated earthquake ruptures

Ma et al 2008

>10

3 4 5 6 7 8 9 10 2 4 6 8 10 L / W Mw

SRCMOD Wells and Coppersmith, 1994 Henry and Das, 2001 Strike-slip Dip-slip

Ishii et al 2005

2004 Mw 9.3 Sumatra 2004 Mw 6 Parkfield

Elongated earthquake ruptures

Galis et al 2018

• verview
• Equation of motion for mode III in 3D
• Equation of motion for mode II in 3D
• - Subshear
• - Supershear
• Ruptures of mixture of modes II and III

• verview
• Equation of motion for mode III in 3D
• Equation of motion for mode II in 3D
• - Subshear
• - Supershear
• Ruptures of mixture of modes II and III

http://sdsu-physics.org

Kinematics

sciencenotes.org

Dynamics

F = ma

Newton’s second law

Warm-ups

Slip inversion method

Ide, 1997

Imaged by back-projection

Meng et al. (2016) Hutko (2009)

• Track rupture speed
• High frequency data
• Seismic array

• How to explain observed source kinematics?
• What is the intrinsic earthquake physics?
• How to link kinematics and dynamics of

earthquakes? Questions

Fracture mechanics:

• - connection between kinematics and dynamics

Linear elastic fracture mechanics

Ø Energy balance between energy release rate and fracture energy Ø Rupture speed as a function of distance

Kostrov, Freund, Andrews (60-70s)

Linear elastic fracture mechanics

KI Kostrov, Freund, Andrews (60-70s)

Linear elastic fracture mechanics

KI Kostrov, Freund, Andrews (60-70s)

• Classical LEFM is not “inertial”
• Speed is independent of acceleration

Linear elastic fracture mechanics

L L

Gc vr

Jump of fracture enregy Response immediately

Infinite acceleration

Crack in bounded media

Ø Release elastic energy is linearly proportional to width of strip Ø

Marder (1998) Waves are reflected back LEFM

Goldman et al 2010 Livne et al 2008

Strip experiments

Inertial equation of motion

Inertial equation of motion

F = ma

Acceleration Apparent mess? Force?

1 Classical LEFM links kinematics and dynamics of 2D infinite media, which is not “inertial” 2 The crack-tip-equation-of-motion for 2D strip media is “inertial” Which may control ruptures on 3D bounded fault? 1 or 2 ?

Key points

The dynamics of elongated ruptures:

• - Rupture acceleration (how rupture begins?)
• - Rupture deceleration (how rupture stops?)

Analytical model

Ingredients

• Anti-plane fault embed in 3D full-space
• Uniform elastic properties
• Uniform fault parameters
• Uniform seismogenic width
• Steady-state speed

W

Analytical model

x2 x1 x3

S l i p p r

• f

i l e

Seismogenic width W

Aseismic region Aseismic region Aseismic region Aseismic region

(3 equations)

Analytical model

x2 x1 x3

S l i p p r

• f

i l e

Seismogenic width W

Aseismic region Aseismic region Aseismic region Aseismic region

(3 equations) Reduce to 1 equation

Analytical model

x2 x1 x3

Slip profile

Seismogenic width W

Aseismic region Aseismic region Aseismic region Aseismic region

Sin(k3x3)

(3 equations) Reduce to 1 equation Slip approximation

Analytical model

x2 x1 x3

Slip profile

Seismogenic width W

Aseismic region Aseismic region Aseismic region Aseismic region

Sin(k3x3)

(3 equations) Reduce to 1 equation Slip approximation

Energy release rate

ü Energy release rate G is a constant independent of rupture s peed and distance, i.e., G = G0 ü Gc = G0 à propagate at any speed Gc ≠ G0 ?

Energy balance at rupture tip

Intuitive physical process

• G0 = Gc à ruptures propagate steadily
• G0 > Gc à ruptures accelerate ↑
• G0 < Gc à ruptures decelerate ↓

edennyweb.wordpress.com

Validation from numerical simulations

τ d τ0 τs τd d0

• G0 > Gc à ruptures accelerate ↑
• Gc /G0 plays an important role in controlling

rupture speed

Rupture acceleration

0.0 5 10 15 20 0.2 0.4 0.6 0.8 1.0

vr / vs L / W · a

0.98 0.97 0.99 0.96 0.95 0.94 0.93 0.92 0.9 0.8 0.7 0.6 Gc / G0

2.5D simulations Energy ratio decreases Weng and Ampuero, 2019

• G0 > Gc à ruptures accelerate ↑
• Gc /G0 plays an important role in controlling

rupture speed

Rupture acceleration

0.0 5 10 15 20 0.2 0.4 0.6 0.8 1.0

vr / vs L / W · a

0.98 0.97 0.99 0.96 0.95 0.94 0.93 0.92 0.9 0.8 0.7 0.6 Gc / G0

2.5D simulations Energy ratio decreases Weng and Ampuero, 2019

• G0 > Gc à ruptures accelerate ↑
• Gc /G0 plays an important role in controlling

rupture speed

Rupture acceleration

0.0 5 10 15 20 0.2 0.4 0.6 0.8 1.0

vr / vs L / W · a

0.98 0.97 0.99 0.96 0.95 0.94 0.93 0.92 0.9 0.8 0.7 0.6 Gc / G0

2.5D simulations Energy ratio decreases Weng and Ampuero, 2019

• G0 > Gc à ruptures accelerate ↑
• Gc /G0 plays an important role in controlling

rupture speed

A= π and P= 3

Rupture acceleration

0.0 5 10 15 20 0.2 0.4 0.6 0.8 1.0

vr / vs L / W

1 2 3

vr / vs

0.0 0.2 0.4 0.6 0.8 1.0

vr W / vs

2 / (1 - Gc / G0)

· a b

0.98 0.97 0.99 0.96 0.95 0.94 0.93 0.92 0.9 0.8 0.7 0.6 Gc / G0

2.5D simulations Weng and Ampuero, 2019

0.0 0.2 0.4 0.6 0.8 1.0

vr / vs a v / v

20 10

L / W ·

1.02 1.03 1.01 1.04 1.05 1.06 1.07 1.08 Gc / G0

• G0 < Gc à ruptures decelerate ↓
• Starting speed also plays a role
• Larger rupture speed lead to longer distance

Rupture deceleration

2.5D simulations Weng and Ampuero, 2019

• G0 < Gc à ruptures decelerate ↓
• Starting speed also plays a role
• Larger rupture speed lead to longer distance

Rupture deceleration

2.5D simulations

0.0 0.2 0.4 0.6 0.8 1.0

vr / vs a v / v

20 10

L / W ·

1.02 1.03 1.01 1.04 1.05 1.06 1.07 1.08 Gc / G0

Weng and Ampuero, 2019

1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0

vr / vs vr W / vs

2 / (1-Gc/G0)

· c

• G0 < Gc à ruptures decelerate ↓
• Starting speed also plays a role
• Larger rupture speed lead to longer distance

A= 1.2π P= 2.6

Rupture deceleration

2.5D simulations

0.0 0.2 0.4 0.6 0.8 1.0

vr / vs a v / v

20 10

L / W ·

1.02 1.03 1.01 1.04 1.05 1.06 1.07 1.08 Gc / G0

Weng and Ampuero, 2019

Validation from 3D simulations

0.0 5 10 0.2 0.4 0.6 0.8 1.0

vr / vs L / W

1.06 1.08 1.1 1.03 1.04 Gc / G0

Theoretical curves

0.0 5 10 0.2 0.4 0.6 0.8 1.0

vr / vs L / W

0.95 0.92 0.97 0.9 0.88 0.84 0.7 0.6 Gc / G0 Theoretical curves

Rupture speed Rupture speed Distance Distance Weng and Ampuero, 2019 A= π and P= 3 A= 1.2π P= 2.6

“Inertial” rupture

−0.1 0.0 0.1 0.2 0.0 0.2 0.4 0.6 0.8 1.0

vr / vs a b

10 20 30 40

L / W

0.0 0.2 0.4 0.6 0.8 1.0

vr / vs vr W / vs

2

·

Acceleration Deceleration

• Rupture evolution predicted by rupture-tip-equation-of-motion
• Rupture is also “inertial”

Weng and Ampuero, 2019 asperity barrier

Elongated ruptures in the lab

1 Closed-form energy release rate on 3D bounded fault is a constant: 2 Ruptures on 3D bounded fault are controlled by the theoretical equation for very long ruptures:

Key points

Implications:

• - Rupture potential and final earthquake size
• - Super-cycle

Rupture potential

R1 R2 R3 R4 G0 Gc

Propagation direction 1 4 3 2

asperity barrier asperity barrier

Rupture potential

R1 R2 R3 R4 G0 Gc

Propagation direction 1 4 3 2

asperity barrier asperity barrier “Potential” energy? “Kinetic” energy?

Rupture potential

R1 R2 R3 R4 G0 Gc

Propagation direction 1 4 3 2

asperity barrier asperity barrier “Potential” energy? “Kinetic” energy? Rupture potential

φ(x)

Along strike A(1-Gc/G0)

Determine earthquake size

www.thinglink.com Gravity potential Rupture potential Weng and Ampuero, JGR, in revision

φ(x)

Along strike A(1-Gc/G0)

Determine earthquake size

www.thinglink.com Gravity potential Rupture potential Weng and Ampuero, 2019

φ(x)

Along strike A(1-Gc/G0)

Determine earthquake size

www.thinglink.com Gravity potential Rupture potential Weng and Ampuero, 2019

Super earthquake cycles?

Ø Fault segmentation Ø Maximum magnitude? Villegas-Lanza et al., (2016)

Deeper Creep Segment Creep Runaway

τs

4 8 12 16

τc

t

L / W 4 8 12 16 L / W Stress S i z e i n c r e a s i n g

t

τd

1 - Gc / G0

∞

• Super cycles

Stressing rate: Assumption:

Weng and Ampuero, 2019

• verview
• Equation of motion for mode III in 3D
• Equation of motion for mode II in 3D
• - Subshear
• - Supershear
• Ruptures of mixture of modes II and III

In-plane sub-shear

0.0 5 10 15 20 0.2 0.4 0.6 0.8 1.0

vr / vs L / W v W / v / (1 - G / G ) ·

0.98 0.97 0.99 0.96 0.95 0.94 0.93 0.92 0.9 0.8 0.7 0.6 Theoretical curves Gc / G0

Rayleigh speed

Weng and Ampuero, In prep. Analytic result (similar as mode III):

In-plane sub-shear

1 2 3 4 5 0.0 5 10 15 20 0.2 0.4 0.6 0.8 1.0

vr / vs L / W vr / vs

0.0 0.2 0.4 0.6 0.8 1.0

vr W / vs

2 / (1 - Gc / G0)

·

0.98 0.97 0.99 0.96 0.95 0.94 0.93 0.92 0.9 0.8 0.7 0.6 Theoretical curves Gc / G0

Rayleigh speed

A= 1.5π and P= 3.5 Weng and Ampuero, In prep. Analytic result (similar as mode III):

• verview
• Equation of motion for mode III in 3D
• Equation of motion for mode II in 3D
• - Subshear
• - Supershear
• Ruptures of mixture of modes II and III

Dynamics of supershear ruptures

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 5 10 15 20

vr / vs L / W

• Steady-state supershear
• Gc/G0 controls supershear

speed

• Critical value of Gc/G0 for

supershear 3D numerical simulations

Critical Gc/Gc S wave speed Weng and Ampuero, In manuscript. Eshelby speed

Dynamics of supershear ruptures

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 5 10 15 20

vr / vs L / W

3D numerical simulations Analytical work:

Critical Gc/Gc S wave speed Weng and Ampuero, In manuscript. P wave speed S wave speed G0

sup

Gc Eshelby speed

• verview
• Equation of motion for mode III
• Equation of motion for mode II
• - Subshear
• - Supershear
• Ruptures of mixture of modes II and III

Bao et al, 2019

2018 Mw7.5 Palu earthquake

4.1 km/s

Sub-Rayleigh Supshear Rupture speed Unstable vE vP vS vR

Modes II (strike slip)

Slow supershear (sub-Eshelby)

2018 Palu earthquake

Slow supershear (sub-Eshelby)

Huang et al, 2016

Non-pure strike slip

Socquet et al (2019) 2018 Palu earthquake

• How to explain the observed slow supershear

earthquakes?

• What is the effects of rake angle (mixture of

modes II and III) on dynamic ruptures?

Mixture of modes II and III

Strike Slip

Rake

W

Real speed Horizontal speed ∆t ∆t Rupture front Rupture front

a b

Slow supershear (sub-Eshelby)

0.0 0.5 1.0 1.5 vr / vS L / W 5

40 20

10 15 L / W 5 10 15 Real speed Horizontal speed

Rake angle

vR vS vE vR vS vE

a b

Geometrical effects?

Strike Slip

Rake

vII / vS = 1.732 vIII / vS= 1.0

Elliptical front

10 20

Rupture time (s) Kinematic model 2 4 6 8 1 12 14 16 18 20 22 2 4 6 8 1 12 14 16 18 20 22

Geometrical effects?

Strike Slip

Rake

vII / vS = 1.732 vIII / vS= 1.0

Elliptical front

10 20

Rupture time (s) Kinematic model 2 4 6 8 1 12 14 16 18 20 22 2 4 6 8 1 12 14 16 18 20 22

0.00 10 20 30 40 50 10 20 30 40 50 0.5 1.0 1.5 vr / vS Rake angle Rake angle vR vS vE vR vS vE

Kinematic model Dynamic model

Real speed Horizontal speed

a b

Geometrical effects?

Strike Slip

Rake

vII / vS = 1.732 vIII / vS= 1.0

Elliptical front

10 20

Rupture time (s) Kinematic model 2 4 6 8 1 12 14 16 18 20 22 2 4 6 8 1 12 14 16 18 20 22

00 10 20 30 40 50 10 20 30 40 50 Average angle of front Rake

Kinematic model Dynamic model

0.00 10 20 30 40 50 10 20 30 40 50 0.5 1.0 1.5 vr / vS Rake angle Rake angle vR vS vE vR vS vE

Kinematic model Dynamic model

Real speed Horizontal speed

a b

Ø Slow supershear can partly be explained by geometrical effect

Insight for seismology

. 9 1.1 1.3 1.5 1.7 . 9 1.1 1.3 1.5 1.7 1 . 1 1.3 1.5 1.7 1 . 1 1.3 1.5 1.7

0 0.15 0.20 0.25 0.15 0.20 0.25 10 20 30 40 Rake angle κ κ vr / vS

0.9 1.7

vr / vS

0.9 1.7

Real speed Horizontal speed

Sub-Rayleigh Sub-Rayleigh Sub-Rayleigh Sub-Rayleigh

a b

Energy ratio

Summary

Sub-Rayleigh Supshear Rupture speed Rupture speed Unstable vE vP vS vR

Modes II (strike slip)

Subshear vS

Modes III (dip slip)

Velocity term

For 3D bounded fault

Sub-Rayleigh Supshear Rupture speed Rupture speed Unstable vE vP vS vR

Modes II (strike slip)

Subshear vS

Modes III (dip slip)

Summary

Mixture

For 3D bounded fault